Ascending Numbers Problems

We say a number is ascending if it's digits are strictly increasing. For example, 189 and 3468 are ascending while 142 and 466 are not. For which ascending number n is 6n also ascending?

I have got the answer to this problem after a while with some guess and check, but I would like to know a quicker way to work it out with a proper method. Can you please provide a relatively detailed explanation.